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Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood

Author

Listed:
  • Vanessa Berenguer-Rico

    (Department of Economics, University of Oxford)

  • Søren Johansen

    (Department of Economics, University of Copenhagen, Denmark)

  • Bent Nielsen

    (Department of Economics, University of Oxford)

Abstract

The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to fi?nd, for a given h; a sub-sample of h '?good' ?observations among n observations and estimate the regression on that sub-sample. We fi?nd models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be h1/2 consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.

Suggested Citation

  • Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood," Discussion Papers 19-11, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1911
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    File URL: https://www.economics.ku.dk/research/publications/wp/dp_2019/1911.pdf
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    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Jurgen A. Doornik, 2016. "An Example of Instability: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 357-359, June.
    3. Vanessa Berenguer Rico & Ines Wilms, 2018. "White heteroscedasticty testing after outlier removal," Economics Series Working Papers 853, University of Oxford, Department of Economics.
    4. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals," CREATES Research Papers 2019-12, Department of Economics and Business Economics, Aarhus University.
    5. Rousseeuw, Peter & Perrotta, Domenico & Riani, Marco & Hubert, Mia, 2019. "Robust Monitoring of Time Series with Application to Fraud Detection," Econometrics and Statistics, Elsevier, vol. 9(C), pages 108-121.
    6. Jurgen A. Doornik & David F. Hendry, 2016. "Outliers and Model Selection: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 360-365, June.
    7. Vanessa Berenguer Rico & Bent Nielsen, 2017. "Marked and Weighted Empirical Processes of Residuals with Applications to Robust Regressions," Economics Series Working Papers 841, University of Oxford, Department of Economics.
    8. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.
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    More about this item

    Keywords

    Chebychev estimator; LMS; Uniform distribution; Least squares estimator; LTS; Normal distribution; Regression; Robust statistics;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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